There could be many reasons behind can’t sign in into AOL mail. AOL customer service is also very responsive and helpful you may contact AOL Support at any time. Follow a few simple steps to make sure you have really an issue with AOL mail-

First, you need to check your internet connection is working or not.
Confirm again and make sure you are typing correct username and password. Sometimes password could be case sensitive.
Clear your cookies and cache from the browser by reading https://support.google.com/accounts/answer/9098093?co=GENIE.Platform=Desktop&hl=en&visit_id=636734655770807590-1653639453&rd=1
In case of if you are using any type of virtual private network (VPN) please stop that.
Some antivirus protection and firewalls also block accessing email packets. So try to access email by disabling them.
Most of the time these above steps works. If you have still issue mark below in comments.

First, all the program’s security setting must be the default mode. I had the same issue and it caused by the bad cache in my browser.

I will recommend you to clean your browser cache. If you don’t know how to clean it follow simple steps below-

Open your google chrome browser. At the right top corner click on three verticle dots.
Now go to settings and select advance from the very bottom of the screen.
Here need to click on “Clear Browsing Data” and choose time duration since you are having the issue.
Now click on clear data and it will delete all the cookies and cache saved in your browser.
Now try to access your mail. If still having the problem you have to reset your whole browser as factory default. Mark a comment below if needed, I will give that step too.